Of the replacement from inside the (1), i have:
So it example of Bayes’ Theorem deals with the easy situation in which you’ve got a couple of hypotheses H and J that are collectively private and you will jointly exhaustive, and you may where you’re selecting \(\Pr(H \middle Age)\), that’s, your chances one to H is true provided proof E. What that it illustration of Bayes’ Theorem does is actually offer one with a means of calculating one chances, provided one understands, first, \(\Pr(H)\) and you may \(\Pr(J)\)-which is, the brand new good priori logical probabilities of \(H\) and you will \(J\)-and get, 2nd, \(\Pr(E \mid H)\) and you can \(\Pr(Age \mid J)\)-which is, the fresh new analytical probability of \(E\) provided, correspondingly, just \(H\) and just \(J\).
But now Draper brings up two substantive states. The first is that the an effective priori likelihood of the new hypothesis away from indifference is not below the brand new an effective priori likelihood of theism, making sure that we have
Draper’s next substantive claim is that the conjunction of propositions throughout the fulfillment and you can aches to which Draper refers, and you can that’s depicted of the \(O\)’ is more apt to be real should your hypothesis of indifference holds true than just if theism is valid. Therefore we has actually
However, so long as \(\Pr(T)\) and you will \(\Pr(O \middle T)\) are not equivalent to zero-which is seriously affordable-(5) and you may (6) are going to be rewritten once the
Therefore we have the results that, given the factual statements about satisfaction and pain summarized by the \(O\)’, theism is more apt to be incorrect rather than end up being true.
